President Donald Trump urged Democrats on Wednesday to "put partisanship aside" as he bluntly warned them against using their newfound control of the US House of Representatives to tie up his administration in investigations.

"It was a big day yesterday, an incredible day," Trump said following Tuesday's midterm election in which Republicans lost the House but increased their hold on the Senate.

"I think people like the job I'm doing," Trump told a free-wheeling news conference at the White House which featured several acrimonious exchanges with reporters.

Democrats will have around 229 seats in the 435-member House, while Republicans will hold 53 seats in the 100-member Senate, up from 51, according to projections by The New York Times.

Trump offered an olive branch to Democrats, praising their leader and likely next House speaker Nancy Pelosi and saying "I really believe that we have the chance to get along really well with the Democrats."

"It is time for members of both parties to join together, put partisanship aside, and keep the American economic miracle going strong."

Trump cited health care and infrastructure as areas where the two parties could work together.

But the president warned he would not hesitate to retaliate if House Democrats use their committee powers in the next Congress to investigate members of his administration or his personal finances.

"They can play that game," he said. "All you are going to do is end up in back and forth and back and forth.

"I think that I am better at that game then they are actually," he said.

"Or we can work together," he said, adding that "it really could be a beautiful bipartisan type of situation."

Trump also dismissed the suggestion he could move to end Special Counsel Robert Mueller's ongoing investigation of whether his 2016 election campaign colluded with Russia to get him into the White House.

"I could fire everybody right now, but I don't want to stop it because politically I don't like stopping it," Trump said, calling the probe a "hoax" and a "disgrace".

"It should never have been started because there was no crime," he said. "There's no collusion."

'Very hostile media coverage'

Trump reeled off a shopping list of disadvantages he claimed that the Republicans had faced going into Tuesday's vote, including "wealthy donors and special interests" for the Democrats, and "very hostile media coverage."

At one point during the press conference, a visibly angry Trump branded CNN's White House correspondent Jim Acosta a "rude, terrible person" and an "enemy of the people" in a testy exchange.

"You shouldn't be working for CNN," he said. "When you report fake news, which CNN does a lot, you are the enemy of the people."

Trump also called out Republicans who did not accept his offer of campaign help, saying they failed to accept his "embrace."

"You have some that said, 'Let's stay away, let's stay away.' They did very poorly," Trump said.

Republicans backed by the White House defeated Democratic senators in several states won by Trump in 2016 - Florida, Indiana, Missouri and North Dakota.

The Republican Senate candidate was also leading in Arizona while Democrats picked up a Republican Senate seat in Nevada.

Democrats gained seven governorships but fell short in a high-profile race in Florida, which - as Trump noted on Wednesday - is expected to play a key role in the 2020 presidential election.

With the House victory, Democrats will take over committees, giving them the power to hold hearings, call witnesses and issue subpoenas to administration officials.

"We will conduct the investigations that Republicans wouldn't conduct," Democratic Representative Eric Swalwell of California said on NBC's "Today" show.

"We'll fill in the gaps on the Russia investigations," he said of the Mueller probe. "American people will see (Trump's) tax returns."

'Collegial place'

Senate majority leader Mitch McConnell said he expected the president would be able to work with a divided Congress.

"The Senate is a pretty collegial place and even though we had big differences over things like taxes and judges, there were plenty of other things we did together and no reason that would stop simply because the House now becomes Democratic," he said.

"We're certainly going to try to help the president achieve what he would like with the (US-Mexico) wall," McConnell said.

Pelosi, who is likely to return as House speaker despite opposition from some centrist Democrats, promised that the party will serve as a counterweight - but also work with Trump.

"Today is more than about Democrats and Republicans. It's about restoring the constitution's checks and balances to the Trump administration," Pelosi said.

But she added: "A Democratic Congress will work for solutions that bring us together, because we have all had enough of division."

Like in the 2016 presidential election, rural areas went heavily for Republicans on Tuesday while urban areas broke towards the Democrats.

More women than men voted for Democrats, according to exit polls, particularly white suburban women, and the new House will feature a record number of women lawmakers.

But the rosiest expectations of some Democrats -- that they could create a "blue wave" even when playing defense on the Senate map -- proved unfounded.